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Understanding human vision not only involves empirical descriptions of how it works, but also organization
principles that explain why it does so. Identifying the guiding principles of visual phenomena requires learning
algorithms to optimize specific goals. Moreover, these algorithms have to be flexible enough to account for the
non-linear and adaptive behavior of the system.
For instance, linear redundancy reduction transforms certainly explain a wide range of visual phenomena.
However, the generality of this organization principle is still in question:10 it is not only that and additional
constraints such as energy cost may be relevant as well, but also, statistical independence may not be the better
solution to make optimal inferences in squared error terms. Moreover, linear methods cannot account for the
non-uniform discrimination in different regions of the image and color space: linear learning methods necessarily
disregard the non-linear nature of the system. Therefore, in order to account for the non-linear behavior,
principled approaches commonly apply the trick of using (already non-linear) parametric expressions taken from
empirical models. Therefore these approaches are not actually explaining the non-linear behavior, but just
fitting it to image statistics. In summary, a proper explanation of the behavior of the system requires flexible
unsupervised learning algorithms that (1) are tunable to different, perceptually meaningful, goals; and (2) make
no assumption on the non-linearity.
Over the last years we have worked on these kind of learning algorithms based on non-linear ICA,18 Gaussianization,
19 and principal curves. In this work we stress the fact that these methods can be tuned to
optimize different design strategies, namely statistical independence, error minimization under quantization, and
error minimization under truncation. Then, we show (1) how to apply these techniques to explain a number of
visual phenomena, and (2) suggest the underlying organization principle in each case.
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